Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14524068 | C2 | semidirect |
| 2. C2×#14524068 | C2 | semidirect |
| 3. #16864163 | C2 | semidirect |
| 4. #16863664 | C2 | semidirect |
| 5. #16863661 | C2 | semidirect |
| 6. #16863444 | C2 | semidirect |
| 7. #16863380 | C2 | semidirect |
| 8. C2×#14523959 | C2 | semidirect |
| 9. #575×C67 | C2 | semidirect |
| 16. C2×#11761615 | C22 | semidirect |
| 18. C2×#11761613 | C22 | semidirect |
| 20. #14524050 | C22 | semidirect |
| 25. #14523978 | C22 | semidirect |
| 26. #14523962 | C22 | semidirect |
| 27. #14523960 | C22 | semidirect |
| 28. #14523959 | C22 | semidirect |
| 32. #137×C67 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C67 | C22 | semidirect |
| 148. C67 | #3068 | semidirect |
| 149. #575 | D67 | semidirect |
| 162. #137 | C2×D67 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D67 | semidirect |